The IMABS function in Google Sheets is a powerful tool used for mathematical calculations involving complex numbers. It simplifies the process of obtaining the absolute or magnitude of a complex number, returning a real number that represents this magnitude. This function is particularly useful in fields such as engineering, physics, and finance, where complex numbers frequently appear in calculations.

Syntax

IMABS(complex_number)

• complex_number: This is the complex number for which you want to find the absolute value. It can be entered as a text string in the form “a+bi” or “a-bi”, where a is the real part and b is the imaginary part.

Example #1

IMABS("3+4i")

This function calculates the absolute value of the complex number 3+4i. The result would be 5, as the absolute value is determined through the formula √(a² + b²).

Example #2

IMABS("-1-1i")

In this case, the function determines the absolute value of the complex number -1-1i, which would result in approximately 1.4142, as calculated by √((-1)² + (-1)²).

Example #3

IMABS("0+5i")

Here, the absolute value of the complex number 0+5i is computed, yielding a result of 5, since the real part is 0 and only the imaginary part contributes to the magnitude.

Error handling

• VALUE!: This error indicates that the input provided is not a valid complex number format.
• NUM!: This error suggests that the function encountered an invalid numeric result, possibly due to improper input values.
• REF!: This error occurs when the referenced complex number is invalid or does not exist in the specified context.

Conclusion

The IMABS function is essential for anyone working with complex numbers in Google Sheets. It allows users to effortlessly obtain the absolute value, making it an indispensable tool in various analytical scenarios. By understanding its syntax, usage, and potential error responses, users can effectively integrate this function into their workflows.